Physics topic to write about for a mathematics class?

[Mary]

So, I am currently in an Advanced Calculus class (ie. elementary analysis of calculus). Our end project is to write a 5-6 page paper on a topic of our choice and relate it back to the class. A lot of the other students are economics majors so they are picking economic topics. I'm a physics major so I, of course, want to pick a physics topic.

I was wondering if anyone had any good ideas for topics? I was thinking of working on the topic of chaos theory because its very interesting but its not necessarily a physics topic. I want to challenge myself. I have previously done projects on chaos theory and the neurophysics of consciousness and now I feel like I can't think of anything else interesting. I would appreciate any ideas! Thanks a bunch.

 

[Simon Bridge]

It would help if it was related to calculus I suppose.
What are the physical fields that interest you?

 

[Dishsoap]

How would you relate chaos theory back to the class?

One thing I always found interesting is how Newton derived the kinematic equations, since he had to, you know, invent calculus to do it. Maybe that would be an interesting topic?

 

[Simon Bridge]

Flux Calculus:
Newton I. (1671) Methodus Fluxionum et Serierum Infinitarum.
https://archive.org/details/methodoffluxions00newt
... the fact of continuous motion was used to formalize calculus, but he'd got the idea from work done on infinite series.
Seeing how people actually worked stuff out is quite fun though.

Also compare how Leibnitz managed it.
But really for history buffs.

 

[mpresic]

Feynman's path integral might be a good idea. Some elements of it reminded me of Lesbegue integration when I first encountered path integrals. See Feynman and Hibbs Path integrals, Barry Holstein also wrote a good textbook. Original papers by Feynman written in the late 1940's seem to be good as well, but Feynman and Hibbs is more introductory

 

[Mary]

RE

Yes, I was also thinking of using Newton's derivations to get some ideas. Supposedly, there has been evidence that he stole most of his ideas from Hooke. I always thought that was pretty interesting. That also leads me to think that I may go more into the history of it than the math. I have a hard time staying focused when I'm really interested in a subject that can spread out quickly haha. Thanks for all of the ideas so far.

I also thought chaos would be hard to relate back to the advanced calc course. Although, it would have some really nice images to share.

 

[jasonRF]

What makes sense depends a lot on your interests, level of physics you have learned, and how rigorous the paper needs to be (this course does cover topics such as uniform continuity, uniform convergence, etc., yes?). Here are a few topics that may or may not make sense for you - I was trying to think about topics that could have some real math involved yet be interesting to a physicist:

1) physics is waves, wave propagation, etc. Could use as a motivator for Fourier series; discussing convergence of the series would fit in nicely with an intro analysis class like you are taking.

2) physics could be electrostatics, quantum mechanics, etc; the math of interest could be Dirac delta function and perhaps its derivatives. This may be a bit much to take on, as you would have learn basic distribution theory. The version the matheticians like is presented nicely in resources such as Strichartz' book "a guide to distribution theory and Fourier transforms" (written as much for scientists as for mathematicians), or the first chapter or two of "applied functional analysis" by Griffel, or perhaps the version many physicists like as presented in Lighthill's "Fourier analysis and generalised functions". Check your library.

3) If you have learned anything about variational principles / calculus of variations in mechanics or other courses this could be interesting. If you need to make it rigorous it may be too much, though (I have never even looked at a rigorous treatment).

I hope you find something fun to write about!

jason

 

[Mary]

It would help if it was related to calculus I suppose.
What are the physical fields that interest you?

I have done a lot of undergraduate research in relation to optics and infinite lens systems.

But, I have also wanted to have more experience with mechanical systems. Does anyone know of an interesting mechanical system that I could apply elementary analysis too? ...maybe a gyroscope? or maybe even an engine? I don't know if this would be to complex for a 5 page paper.I forgot to mention that the professor is requiring us to base our paper off of another one so I need to send him a paper. I guess this makes it easier but I feel like I don't get to be as "creative" with it.

 

[jasonRF]

What do you mean when you say "apply elementary analysis to?" Are you expected to do proofs that series convergence, integrals exist, etc?

One idea is to search in the American Journal of Physics for topics that interest you; it often has not-so-advanced papers that are very interesting but intended to show derivations or applications for use in undergrad physics courses. You should find papers on nonlinear vibrations and such in that journal as well.

jason

 

[epenguin]

Chaos theory seems what is most likely to interest an interdisciplinary class, especially of economists. You won't be able to do much in 5 pages so try think of an aspect which gives nice simulation pictures.

 

[micromass]

Do some calculus of variations? For example, solve the brachistochrone problem and other related ones?